WBM-DLNets: Wrapper-Based Metaheuristic Deep Learning Networks Feature Optimization for Enhancing Brain Tumor Detection

This study presents wrapper-based metaheuristic deep learning networks (WBM-DLNets) feature optimization algorithms for brain tumor diagnosis using magnetic resonance imaging. Herein, 16 pretrained deep learning networks are used to compute the features. Eight metaheuristic optimization algorithms, namely, the marine predator algorithm, atom search optimization algorithm (ASOA), Harris hawks optimization algorithm, butterfly optimization algorithm, whale optimization algorithm, grey wolf optimization algorithm (GWOA), bat algorithm, and firefly algorithm, are used to evaluate the classification performance using a support vector machine (SVM)-based cost function. A deep-learning network selection approach is applied to determine the best deep-learning network. Finally, all deep features of the best deep learning networks are concatenated to train the SVM model. The proposed WBM-DLNets approach is validated based on an available online dataset. The results reveal that the classification accuracy is significantly improved by utilizing the features selected using WBM-DLNets relative to those obtained using the full set of deep features. DenseNet-201-GWOA and EfficientNet-b0-ASOA yield the best results, with a classification accuracy of 95.7%. Additionally, the results of the WBM-DLNets approach are compared with those reported in the literature.


Introduction
Uncontrolled cell development causes brain abnormalities, such as brain tumors. This syndrome has been associated with a considerable number of deaths worldwide and is commonly recognized as a lethal disease [1]. Brain tumors, whether benign or malignant, cause damage to adjacent brain tissue owing to the increased pressure exerted on the skull [2]. In 2022, approximately 88,970 people suffered brain tumors, among which 63,040 were benign, whereas the remaining 25,930 were malignant [3,4]. Gliomas, meningiomas, and pituitary gland tumors are several types of tumors that may affect the human brain [5,6]. Hence, the early detection of brain tumors is critical for timely and efficient treatment.
Neuro-oncologists can effortlessly and rapidly diagnose brain tumors using computeraided diagnostic (CAD) technologies. The development of new imaging technologies, such as magnetic resonance imaging (MRI), to visualize the characteristics of brain tumors has increased in recent years. MRI is a useful technique that offers detailed scans of tissues and organs. Owing to its noninvasive nature, MRI is the most reliable method for locating and 98% and 97.2% for brain tumor detection, respectively [30,31]. Training a pretrained model requires considerable time. To address this problem, a study computed deep features using pretrained networks and utilized them to train conventional classifiers [32]. The concatenated deep features of ShuffleNet V2, DenseNet-169, and MnasNet yielded an accuracy of 93.72% using the SVM model. However, reportedly, the training time of the model was prolonged because of the large size of the training feature vectors. Therefore, the feature removal technique can be applied to improve model accuracy. Dokeroglu et al. [33] recently examined different wrapper-based feature-selection approaches. Wrapper techniques investigate the performance of each feature subset and combine a metaheuristic optimization algorithm with a classifier.
Therefore, in this study, wrapper-based metaheuristic deep-learning network (WBM-DLNet) feature optimization approaches were investigated to improve the classification accuracy of brain MRI scans. First, brain MRI scans were preprocessed to resize and reduce noise. Various pretrained models, such as DarkNet-19, DarkNet-53, DenseNet-201, EfficientNet-b0, GoogLeNet365, GoogLeNet, Inception-ResNet-v2, Inception-v3, MobileNet-v2, NASNet-Mobile, ResNet-101, ResNet-50, ResNet-18, Shuf-fleNet, SqueezeNet, and Xception, were used to extract information from brain MRI images. Wrapper approaches with various metaheuristic optimization algorithms, such as the marine predators algorithm (MPA), atom search optimization algorithm (ASOA), Harris hawks optimization algorithm (HHOA), butterfly optimization algorithm (BOA), whale optimization algorithm (WOA), grey wolf optimization algorithm (GWOA), bat algorithm (BA), and firefly algorithm (FA), were used to examine the classification performance using SVM. An empirical approach was used to select the best network. Based on the results of various feature subsets, a new concatenated feature vector was formed to evaluate the performance. The performance of the proposed framework was evaluated using an online brain MRI dataset.

Brain MRI Dataset
In this study, a collection of brain MRI images available online was used. The dataset utilized herein was retrieved from the Kaggle website [34] and comprised four brain MRI classes. Table 1 presents information on the brain MRI dataset. Table 1. Details of online brain MRI dataset.

Glioma Tumor Meningioma Tumor No Tumor Pituitary Tumor
Brain MRI images accuracy of 95.56% for tertiary class problems (glioma, meningioma, and pituitary gland tumor) [28]. Subsequently, the authors applied data augmentation to balance the data; nevertheless, the use of data augmentation in real-time applications was unreliable. A 25layer deep learning network reported an accuracy of 92.66% [29]. Pretrained networks, such as GoogleNet and ResNet-50, also reported classification accuracies of 98% and 97.2% for brain tumor detection, respectively [30,31]. Training a pretrained model requires considerable time. To address this problem, a study computed deep features using pretrained networks and utilized them to train conventional classifiers [32]. The concatenated deep features of ShuffleNet V2, DenseNet-169, and MnasNet yielded an accuracy of 93.72% using the SVM model. However, reportedly, the training time of the model was prolonged because of the large size of the training feature vectors. Therefore, the feature removal technique can be applied to improve model accuracy. Dokeroglu et al. [33] recently examined different wrapper-based feature-selection approaches. Wrapper techniques investigate the performance of each feature subset and combine a metaheuristic optimization algorithm with a classifier. Therefore, in this study, wrapper-based metaheuristic deep-learning network (WBM-DLNet) feature optimization approaches were investigated to improve the classification accuracy of brain MRI scans. First, brain MRI scans were preprocessed to resize and reduce noise. Various pretrained models, such as DarkNet-19, DarkNet-53, DenseNet-201, EfficientNet-b0, GoogLeNet365, GoogLeNet, Inception-ResNet-v2, Inception-v3, MobileNet-v2, NASNet-Mobile, ResNet-101, ResNet-50, ResNet-18, ShuffleNet, SqueezeNet, and Xception, were used to extract information from brain MRI images. Wrapper approaches with various metaheuristic optimization algorithms, such as the marine predators algorithm (MPA), atom search optimization algorithm (ASOA), Harris hawks optimization algorithm (HHOA), butterfly optimization algorithm (BOA), whale optimization algorithm (WOA), grey wolf optimization algorithm (GWOA), bat algorithm (BA), and firefly algorithm (FA), were used to examine the classification performance using SVM. An empirical approach was used to select the best network. Based on the results of various feature subsets, a new concatenated feature vector was formed to evaluate the performance. The performance of the proposed framework was evaluated using an online brain MRI dataset.

Brain MRI Dataset
In this study, a collection of brain MRI images available online was used. The dataset utilized herein was retrieved from the Kaggle website [34] and comprised four brain MRI classes. Table 1 presents information on the brain MRI dataset. accuracy of 95.56% for tertiary class problems (glioma, meningioma, and pituitary gland tumor) [28]. Subsequently, the authors applied data augmentation to balance the data; nevertheless, the use of data augmentation in real-time applications was unreliable. A 25layer deep learning network reported an accuracy of 92.66% [29]. Pretrained networks, such as GoogleNet and ResNet-50, also reported classification accuracies of 98% and 97.2% for brain tumor detection, respectively [30,31]. Training a pretrained model requires considerable time. To address this problem, a study computed deep features using pretrained networks and utilized them to train conventional classifiers [32]. The concatenated deep features of ShuffleNet V2, DenseNet-169, and MnasNet yielded an accuracy of 93.72% using the SVM model. However, reportedly, the training time of the model was prolonged because of the large size of the training feature vectors. Therefore, the feature removal technique can be applied to improve model accuracy. Dokeroglu et al. [33] recently examined different wrapper-based feature-selection approaches. Wrapper techniques investigate the performance of each feature subset and combine a metaheuristic optimization algorithm with a classifier. Therefore, in this study, wrapper-based metaheuristic deep-learning network (WBM-DLNet) feature optimization approaches were investigated to improve the classification accuracy of brain MRI scans. First, brain MRI scans were preprocessed to resize and reduce noise. Various pretrained models, such as DarkNet-19, DarkNet-53, DenseNet-201, EfficientNet-b0, GoogLeNet365, GoogLeNet, Inception-ResNet-v2, Inception-v3, MobileNet-v2, NASNet-Mobile, ResNet-101, ResNet-50, ResNet-18, ShuffleNet, SqueezeNet, and Xception, were used to extract information from brain MRI images. Wrapper approaches with various metaheuristic optimization algorithms, such as the marine predators algorithm (MPA), atom search optimization algorithm (ASOA), Harris hawks optimization algorithm (HHOA), butterfly optimization algorithm (BOA), whale optimization algorithm (WOA), grey wolf optimization algorithm (GWOA), bat algorithm (BA), and firefly algorithm (FA), were used to examine the classification performance using SVM. An empirical approach was used to select the best network. Based on the results of various feature subsets, a new concatenated feature vector was formed to evaluate the performance. The performance of the proposed framework was evaluated using an online brain MRI dataset.

Brain MRI Dataset
In this study, a collection of brain MRI images available online was used. The dataset utilized herein was retrieved from the Kaggle website [34] and comprised four brain MRI classes. Table 1 presents information on the brain MRI dataset. accuracy of 95.56% for tertiary class problems (glioma, meningioma, and pituitary gland tumor) [28]. Subsequently, the authors applied data augmentation to balance the data; nevertheless, the use of data augmentation in real-time applications was unreliable. A 25layer deep learning network reported an accuracy of 92.66% [29]. Pretrained networks, such as GoogleNet and ResNet-50, also reported classification accuracies of 98% and 97.2% for brain tumor detection, respectively [30,31]. Training a pretrained model requires considerable time. To address this problem, a study computed deep features using pretrained networks and utilized them to train conventional classifiers [32]. The concatenated deep features of ShuffleNet V2, DenseNet-169, and MnasNet yielded an accuracy of 93.72% using the SVM model. However, reportedly, the training time of the model was prolonged because of the large size of the training feature vectors. Therefore, the feature removal technique can be applied to improve model accuracy. Dokeroglu et al. [33] recently examined different wrapper-based feature-selection approaches. Wrapper techniques investigate the performance of each feature subset and combine a metaheuristic optimization algorithm with a classifier. Therefore, in this study, wrapper-based metaheuristic deep-learning network (WBM-DLNet) feature optimization approaches were investigated to improve the classification accuracy of brain MRI scans. First, brain MRI scans were preprocessed to resize and reduce noise. Various pretrained models, such as DarkNet-19, DarkNet-53, DenseNet-201, EfficientNet-b0, GoogLeNet365, GoogLeNet, Inception-ResNet-v2, Inception-v3, MobileNet-v2, NASNet-Mobile, ResNet-101, ResNet-50, ResNet-18, ShuffleNet, SqueezeNet, and Xception, were used to extract information from brain MRI images. Wrapper approaches with various metaheuristic optimization algorithms, such as the marine predators algorithm (MPA), atom search optimization algorithm (ASOA), Harris hawks optimization algorithm (HHOA), butterfly optimization algorithm (BOA), whale optimization algorithm (WOA), grey wolf optimization algorithm (GWOA), bat algorithm (BA), and firefly algorithm (FA), were used to examine the classification performance using SVM. An empirical approach was used to select the best network. Based on the results of various feature subsets, a new concatenated feature vector was formed to evaluate the performance. The performance of the proposed framework was evaluated using an online brain MRI dataset.

Brain MRI Dataset
In this study, a collection of brain MRI images available online was used. The dataset utilized herein was retrieved from the Kaggle website [34] and comprised four brain MRI classes. Table 1 presents information on the brain MRI dataset. accuracy of 95.56% for tertiary class problems (glioma, meningioma, and pituitary gland tumor) [28]. Subsequently, the authors applied data augmentation to balance the data; nevertheless, the use of data augmentation in real-time applications was unreliable. A 25layer deep learning network reported an accuracy of 92.66% [29]. Pretrained networks, such as GoogleNet and ResNet-50, also reported classification accuracies of 98% and 97.2% for brain tumor detection, respectively [30,31]. Training a pretrained model requires considerable time. To address this problem, a study computed deep features using pretrained networks and utilized them to train conventional classifiers [32]. The concatenated deep features of ShuffleNet V2, DenseNet-169, and MnasNet yielded an accuracy of 93.72% using the SVM model. However, reportedly, the training time of the model was prolonged because of the large size of the training feature vectors. Therefore, the feature removal technique can be applied to improve model accuracy. Dokeroglu et al. [33] recently examined different wrapper-based feature-selection approaches. Wrapper techniques investigate the performance of each feature subset and combine a metaheuristic optimization algorithm with a classifier. Therefore, in this study, wrapper-based metaheuristic deep-learning network (WBM-DLNet) feature optimization approaches were investigated to improve the classification accuracy of brain MRI scans. First, brain MRI scans were preprocessed to resize and reduce noise. Various pretrained models, such as DarkNet-19, DarkNet-53, DenseNet-201, EfficientNet-b0, GoogLeNet365, GoogLeNet, Inception-ResNet-v2, Inception-v3, MobileNet-v2, NASNet-Mobile, ResNet-101, ResNet-50, ResNet-18, ShuffleNet, SqueezeNet, and Xception, were used to extract information from brain MRI images. Wrapper approaches with various metaheuristic optimization algorithms, such as the marine predators algorithm (MPA), atom search optimization algorithm (ASOA), Harris hawks optimization algorithm (HHOA), butterfly optimization algorithm (BOA), whale optimization algorithm (WOA), grey wolf optimization algorithm (GWOA), bat algorithm (BA), and firefly algorithm (FA), were used to examine the classification performance using SVM. An empirical approach was used to select the best network. Based on the results of various feature subsets, a new concatenated feature vector was formed to evaluate the performance. The performance of the proposed framework was evaluated using an online brain MRI dataset.

Brain MRI Dataset
In this study, a collection of brain MRI images available online was used. The dataset utilized herein was retrieved from the Kaggle website [34] and comprised four brain MRI classes. Table 1 presents information on the brain MRI dataset.

Preprocessing
Preprocessing is required to eliminate unnecessary information and reduce noise from brain MRI scans. Cropping is typically employed for removing nonbrain regions and reducing noise. In this study, a cropping approach was employed to compute the extreme points of the brain area. Dilation and erosion processes, the two fundamental morphological processes, were applied to reduce noise. In an image, dilation involves adding pixels to object borders, whereas erosion involves removing pixels from object boundaries. The size and shape of the structuring element used to process the image determine the number of pixels added to or subtracted from the objects. Additional information on the preprocessing can be found in [32,35]. In addition, the preprocessed images were scaled to meet the input requirements of the pretrained networks employed in this study.

Deep Feature Extraction
Features are the primary factors when categorizing images. Identifying essential features is vital for improving classification performance. Although brain MRI feature extraction can be performed manually or using a deep learning network, manual extraction is very time-consuming. The considerable diversity in brain MRI scans determines their accuracy. By contrast, deep learning neural networks employ a combination of convolutional, pooling, and fully connected layers to build the model. Pretrained deep learning models can extract deep features using the transfer learning method when the dataset is sufficiently small. Figure 1 illustrates the concept of deep feature extraction using a trained model (GoogLeNet). morphological processes, were applied to reduce noise. In an image, dilation invol adding pixels to object borders, whereas erosion involves removing pixels from ob boundaries. The size and shape of the structuring element used to process the im determine the number of pixels added to or subtracted from the objects. Additio information on the preprocessing can be found in [32,35]. In addition, the preproces images were scaled to meet the input requirements of the pretrained networks employ in this study.

Deep Feature Extraction
Features are the primary factors when categorizing images. Identifying essen features is vital for improving classification performance. Although brain MRI feat extraction can be performed manually or using a deep learning network, man extraction is very time-consuming. The considerable diversity in brain MRI sc determines their accuracy. By contrast, deep learning neural networks employ combination of convolutional, pooling, and fully connected layers to build the mod Pretrained deep learning models can extract deep features using the transfer learn method when the dataset is sufficiently small. Figure 1 illustrates the concept of d feature extraction using a trained model (GoogLeNet). Deep neural networks that have been trained on extensive image classification ta are known as pre-trained deep learning models and are capable of extracting hierarch features from images. These deep features are acquired by passing an image through network and analyzing the activation of one or more layers, thus indicating the respo of the network to various image features. These activations may be used to categorize compare images and feed them into other classical machine learning models, such SVM. Deep neural networks that have been trained on extensive image classification tasks are known as pre-trained deep learning models and are capable of extracting hierarchical features from images. These deep features are acquired by passing an image through the network and analyzing the activation of one or more layers, thus indicating the response of the network to various image features. These activations may be used to categorize or compare images and feed them into other classical machine learning models, such as SVM.

Wrapper-Based Feature Selection Approach
Feature selection is essential in numerous machine-learning applications because it affects model accuracy. Therefore, relevant features must be utilized to effectively characterize and classify items. However, the inclusion of irrelevant features may lead to low accuracy. Therefore, the most valuable features must be determined to increase the classification accuracy of the model. During the feature-selection procedure in this study, a subset of a wider set of features was selected to build the machine learning model. Note that a specific criterion is used to assess the quality of the new subset [36]. This can be accomplished using various strategies, such as filter-based, wrapper-based, or embedded feature selection [37]. These approaches can also assist in minimizing model complexity, thus resulting in quicker and more efficient processing.
In this study, wrapper-based algorithms were used to select the most appropriate features for training a machine learning model. Wrapper algorithms are machine learning methods for evaluating the performance of a group of features when used with a particular model (the "wrapper") [38]. The goal of the wrapper is to assess the impact of the selected features on the accuracy of the model. The wrapper algorithm either selects the current subset of features or seeks an improved subset based on the evaluation results. This procedure is repeated until an optimal subset of features is obtained. Figure 2 illustrates the concept of the wrapper approach. For optimal feature selection, this study employed a variety of metaheuristic algorithms and wrapper-based approaches.
grained details. These models can be used in a range of computer vision applicatio as object identification, image segmentation, and image retrieval.

Wrapper-Based Feature Selection Approach
Feature selection is essential in numerous machine-learning applications be affects model accuracy. Therefore, relevant features must be utilized to eff characterize and classify items. However, the inclusion of irrelevant features may low accuracy. Therefore, the most valuable features must be determined to incr classification accuracy of the model. During the feature-selection procedure in th a subset of a wider set of features was selected to build the machine learning mod that a specific criterion is used to assess the quality of the new subset [36]. Thi accomplished using various strategies, such as filter-based, wrapper-based, or em feature selection [37]. These approaches can also assist in minimizing model com thus resulting in quicker and more efficient processing.
In this study, wrapper-based algorithms were used to select the most app features for training a machine learning model. Wrapper algorithms are machine methods for evaluating the performance of a group of features when used particular model (the "wrapper") [38]. The goal of the wrapper is to assess the im the selected features on the accuracy of the model. The wrapper algorithm eithe the current subset of features or seeks an improved subset based on the evaluation This procedure is repeated until an optimal subset of features is obtained. F illustrates the concept of the wrapper approach. For optimal feature selection, th employed a variety of metaheuristic algorithms and wrapper-based approaches.  The goal of metaheuristic techniques is to estimate the solutions to complex problems. They are referred to as "meta" because they integrate multiple low-level heuristics to manage high-level optimization tasks [39]. Examples of metaheuristic algorithms include MPA, ASOA, HHOA, BOA, WOA, GWOA, BA, and FA [33,40]. In wrapper feature selection methods, learning algorithms evaluate the performance of the resulting feature subsets during classification. Metaheuristics are used as search algorithms to identify new optimal subsets [41]. The cost functions of all optimization methods are specified in Equation (1).

Marine Predators Algorithm (MPA)
MPA is an optimization technique inspired by nature that adheres to principles that naturally control the best foraging tactics and encounter rates between predators and prey in marine environments. The hunting and foraging strategies of marine predators, such as sharks and dolphins, serve as the basis for MPA [43,44]. The four key phases used for the simulation are predation, reproduction, migration, and exploration. During the predation phase, the algorithm hunts for and catches food; during the reproduction phase, it transfers genetic material to the progeny; during the exploration phase, it searches for new locations in the search space; and during the migration phase, it relocates the predators to new locations.
Numerous optimization problems, including feature selection, image segmentation, and data clustering, have been effectively solved using this technique. MPA is very efficient and helpful in addressing optimization issues in various fields because it can obtain global optima in complicated search spaces [45].

Atom Search Optimization Algorithm (ASOA)
The principle of ASOA is the mobility and interaction of atoms in a physical system [46]. It is a population-based method in which a group of atoms searches for the best answer in a predetermined search space, and it involves the four key steps of initialization, attraction, repulsion, and migration. During the initialization phase, this method creates a collection of atoms with different positions and velocities in the search space; during the attraction stage, the atoms travel toward the best answer; during the repulsion stage, they move away from one another to explore other regions of the search space; and during the migration step, they relocate to a new location in the search space. Numerous optimization issues have been successfully solved using ASOA [47].

Harris Hawks Optimization Algorithm (HHOA)
Bairathi and Gopalani proposed the optimization technique of HHOA, which is based on the cooperative hunting style of Harris hawks [48]. This algorithm is built on a group of individuals called "hawks" who stand in for potential solutions. The four key phases of HHOA are scouting, prey finding, trap setting, and attacks. During the scouting phase, the program randomly creates an initial population of hawks; during the prey-finding phase, the hawks explore the search space to determine the best answers; during the trap-setting phase, they corner the victim; and during the attack phase, they work together to capture it. Numerous optimization issues have been solved successfully using the HHOA [49].

Butterfly Optimization Algorithm (BOA)
The metaheuristic optimization BOA was developed by Arora and Singh after they studied the feeding habits of butterflies in the environment [50]. The BOA mimics butterfly motion and behavior to explore and adapt to changing search space conditions. It has five stages: initialization, search, selection, mutation, and update. During the initialization stage, this technique randomly creates an initial butterfly population; during the search stage, the butterflies explore the search space and identify the best solutions; during the selection stage, they select the best answers from the population; during the mutation stage, the algorithm introduces random modifications to the selected solutions to explore new search space regions; and during the update stage, the algorithm changes the population, based on the latest solutions discovered during the mutation stage. The BOA has been used to solve various complex engineering problems [51].

Whale Optimization Algorithm (WOA)
Mirjalili and Lewis [52] proposed the WOA in 2016, the WOA is based on the hunting behavior of humpback whales, which hunt in groups and employ bubble nets to catch tiny fish or krill. The WOA algorithm can solve complex optimization problems by discovering the prey, enclosing it, and moving it in spiral bubble-net patterns. The process begins with a random solution. Subsequently, other agents alter their locations by selecting the best search agent and selecting a target for attack, which may be the best search agent or a random whale. The WOA has been successfully used for various optimization issues, including function optimization, scheduling, and data clustering [33].

Grey Wolf Optimization Algorithm (GWOA)
Mirjalili et al. developed the GWOA in 2014 based on the grey wolf social structure and hunting skills [53]. Grey wolves hunt in packs, each headed by an alpha wolf, the dominant member of the crew. The group's second leader, the beta wolf, assists the alpha wolf and conveys the instructions, and the subordinate or delta wolves support. When the prey is within a certain range, the pack surrounds and assaults it. Alpha, beta, and delta wolves are the top three GWOA algorithmic solutions. The remaining wolves are omega wolves and have no bearing on the decisions made in the subsequent iterations. The GWOA employs this social structure and prey-hunting strategies as a mathematical representation to solve optimization issues in domains ranging from computer science to engineering, mathematics, physics, and finance [54,55].

Bat Algorithm (BA)
Yang first presented the BA in 2010 [56] as an optimization technique. This approach is modeled after how bats search for prey by flying randomly, making noise, and listening to echoes [57]. The BA maintains a population of alternative solutions to the optimization problem. It iteratively enhances these solutions using random walk and exploitation procedures. The exploitation operation enables the algorithm to focus on the most promising answers. By contrast, the random-walk operation mimics the unpredictable search behavior of bats. The algorithm also uses a frequency-tuning mechanism motivated by the frequency modulation of bat sounds, which allows it to break out of local optima and discover superior solutions. In addition, the BA is easy to deploy and does not require complicated parameter tuning. Echolocation can be coded as a method for improving the objective function [58].

Firefly Algorithm (FA)
Motivated by the flashing qualities of fireflies, Yang presented the FA in 2010 [59], based on flashes, which attract potential mates and scare away predators. In FA, flashing features are established and used as functions to address combinatorial optimization problems [60]. Fireflies attract fellow flies and move toward brighter fireflies based on their brightness levels. The greater the separation between fireflies, the less enticing they appear to be. In the absence of a brighter light, fireflies travel randomly. Consequently, the intensity of light and appeal levels have key influences on the FA. A specific function can be used to alter brightness at a specific location. Attraction is determined by other fireflies because it is based on the distance and absorption coefficient.

Proposed WBM-DLNets Framework for Brain Tumor Detection
MRI is the most reliable tool used by radiologists for the detection of brain tumors. This study aimed to build an intelligent model that can detect brain tumors and classify them into subcategories (glioma, meningioma, and pituitary gland tumor).
As mentioned in Section 2.2, herein, the input MRIs were preprocessed to eliminate noise and irrelevant information. Next, the pre-trained networks were used to calculate the deep features. The most relevant features were retrieved using MPA-, ASOA-, HHOA-, BOA-, WOA-, GWOA-, BA-, and FA-wrapper-based feature selection techniques. A block diagram of the proposed WBM-DLNets brain tumor detection approach and a flow chart of network selection are shown in Figures 3 and 4, respectively. can be used to alter brightness at a specific location. Attraction is determined by other fireflies because it is based on the distance and absorption coefficient.

Proposed WBM-DLNets Framework for Brain Tumor Detection
MRI is the most reliable tool used by radiologists for the detection of brain tumors. This study aimed to build an intelligent model that can detect brain tumors and classify them into subcategories (glioma, meningioma, and pituitary gland tumor).
As mentioned in Section 2.2, herein, the input MRIs were preprocessed to eliminate noise and irrelevant information. Next, the pre-trained networks were used to calculate the deep features. The most relevant features were retrieved using MPA-, ASOA-, HHOA-, BOA-, WOA-, GWOA-, BA-, and FA-wrapper-based feature selection techniques. A block diagram of the proposed WBM-DLNets brain tumor detection approach and a flow chart of network selection are shown in Figures 3 and 4, respectively.   In the network selection phase, the proposed approach selects deep learning networks with a metaheuristic optimizer having a maximum accuracy of more than 94% for the deep features of an individual deep learning network. Herein, MATLAB's "Jx-WFST," a Jxwrapper feature selection library, was used to implement all methods In the network selection phase, the proposed approach selects deep learning networks with a metaheuristic optimizer having a maximum accuracy of more than 94% for the deep features of an individual deep learning network. Herein, MATLAB's "Jx-WFST," a Jxwrapper feature selection library, was used to implement all methods (https://www.mathworks. com/matlabcentral/fileexchange/84139-wrapper-feature-selection-toolbox, accessed on 7 February 2023). Further, the SVM model was used for brain MRI classification [61,62].

Results and Discussion
In this study, the WBM-DLNet feature optimization technique was applied to enhance the classification accuracy of brain tumor detection. An online brain tumor classification dataset was used to test the presented WBM-DLNets feature optimization technique [34]. Discrimination between the MRI images of the subcategories of tumors was accomplished by utilizing the deep features of various pre-trained deep learning networks, as discussed above. The WBM algorithms discussed above (MPA, ASOA, HHOA, BOA, WOA, GWOA, BA, and FA) were used to extract valuable information. Further, MATLAB 2022b, operating on a personal computer with the following specifications, was used for all processing and analysis: Core i7, 12th Generation, 32 GB of RAM, NVIDIA GeForce RTX 3050, 1 TB SSD, and 64-bit Windows 11. The extracted feature subset was classified using an SVM and 0.2-holdout validation technique. The parameters of each algorithm are listed in Table 2.
For each brain MRI image, the deep features of the various pretrained networks were extracted before the SoftMax layer. The initial rate, number of epochs, and momentum were 0.001, 100, and 0.9, respectively. The results of the full deep features of various pretrained networks are presented as classification accuracy and feature vector size in Figure 5. For each brain MRI image, the deep features of the various pretrained networks were extracted before the SoftMax layer. The initial rate, number of epochs, and momentum were 0.001, 100, and 0.9, respectively. The results of the full deep features of various pretrained networks are presented as classification accuracy and feature vector size in Figure 5. A thorough analysis of the results presented in Figure 4 reveals that the SVM trained using the deep features of DarkNet-53, DenseNet-201, EfficientNet-b0, ResNet-50, and Xception deep-learning networks yielded classification accuracies above 90% for brain MRI images, and the feature vector sizes of these pretrained networks were 1024, 1920, 1280, 2048, and 2048, respectively. EfficientNet-b0 exhibited a classification rate of 92.33% with a training feature vector size of 1280 for brain tumor detection. The results of the various metaheuristic algorithms used to determine the optimal deep features of the various pretrained networks are presented in Table 3. The detailed results of all networks and optimization algorithms in terms of accuracy, feature vector size, and processing time are shown in Figure S1 in the Supplementary Materials. A thorough analysis of the results presented in Figure 4 reveals that the SVM trained using the deep features of DarkNet-53, DenseNet-201, EfficientNet-b0, ResNet-50, and Xception deep-learning networks yielded classification accuracies above 90% for brain MRI images, and the feature vector sizes of these pretrained networks were 1024, 1920, 1280, 2048, and 2048, respectively. EfficientNet-b0 exhibited a classification rate of 92.33% with a training feature vector size of 1280 for brain tumor detection. The results of the various metaheuristic algorithms used to determine the optimal deep features of the various pretrained networks are presented in Table 3. The detailed results of all networks and optimization algorithms in terms of accuracy, feature vector size, and processing time are shown in Figure S1 in the Supplementary Materials.   As presented in Table 3, all optimization algorithms significantly increased and decreased the accuracy and feature vector size, respectively. However, only two deep learning networks (DenseNet-201 and EfficientNet-b0) yielded accuracies greater than 94%. DenseNet-201 with GWOA exhibited almost 3.31% higher accuracy relative to the full features of DenseNet-201 (1920 features). Additionally, it used three times fewer features to train the SVM model (651 features). In the case of EfficientNet-b0, three optimization algorithms, MPA, ASOA, and WOA, classified the brain MRI images with 94.4%, 94.9%, and 94.4% accuracy, respectively. Based on the network selection criteria discussed in Section 3 and Figure 4, the proposed approach selected only the deep features of the EfficientNet-b0-ASOA. The deep features of DenseNet-201-GWOA and EfficientNet-b0-ASOA were concatenated to train the SVM model using the 0.2-holdout and five-fold cross-validation techniques. The confusion metrics of the WBM-DLNets are shown in Figure 6. The results were thoroughly analyzed using the true positive rate (TPR), false negative rate (FNR), positive predictive value (PPV), and false discovery rate (FDR) of the developed machine learning model, as presented in Table 4. Equation (2) can be used to compute TPR, FNR, PPV, FDR, and accuracy.
Bioengineering 2023, 10, x FOR PEER REVIEW 13 of 18 As presented in Table 3, all optimization algorithms significantly increased and decreased the accuracy and feature vector size, respectively. However, only two deep learning networks (DenseNet-201 and EfficientNet-b0) yielded accuracies greater than 94%. DenseNet-201 with GWOA exhibited almost 3.31% higher accuracy relative to the full features of DenseNet-201 (1920 features). Additionally, it used three times fewer features to train the SVM model (651 features). In the case of EfficientNet-b0, three optimization algorithms, MPA, ASOA, and WOA, classified the brain MRI images with 94.4%, 94.9%, and 94.4% accuracy, respectively. Based on the network selection criteria discussed in Section 3 and Figure 4, the proposed approach selected only the deep features of the EfficientNet-b0-ASOA. The deep features of DenseNet-201-GWOA and EfficientNet-b0-ASOA were concatenated to train the SVM model using the 0.2-holdout and five-fold cross-validation techniques. The confusion metrics of the WBM-DLNets are shown in Figure 6. The results were thoroughly analyzed using the true positive rate (TPR), false negative rate (FNR), positive predictive value (PPV), and false discovery rate (FDR) of the developed machine learning model, as presented in Table 4. Equation (2) can be used to compute TPR, FNR, PPV, FDR, and accuracy.  In the case of holdout validation, 159 of the 165 MRI images of glioma tumors were correctly classified and had a TPR of 96.4% (Figure 6a and Table 4). The no-tumor class contained 80 MRI images to test the model. A total of 77 brain MRI images with a PPV of 97.5% were classified correctly. The proposed WBM-DLNets achieved a high classification accuracy of 95.6% with only 1292 feature vector sizes for holdout validation. In the fivefold cross-validation, the proposed model slightly increased the classification accuracy, as presented in Figure 6b and Table 4. The model correctly predicted 811 out of 824 pituitary gland tumor class MRI images with a TPR of 98.1%. Another brain MRI dataset comprising 233 patients was used to validate the adaptability and accuracy [63]. A total of 3064 brain MRI scans were obtained at two hospitals in China (Nanfang Hospital and General Hospital), of which 1426 images comprised glioma tumors, 708 comprised meningioma tumors, and 930 comprised pituitary gland tumors [64]. The results of the proposed approach for the new dataset are presented in Figure 7 and Table 5. In the case of holdout validation, 159 of the 165 MRI images of glioma tumors were correctly classified and had a TPR of 96.4% (Figure 6a and Table 4). The no-tumor class contained 80 MRI images to test the model. A total of 77 brain MRI images with a PPV of 97.5% were classified correctly. The proposed WBM-DLNets achieved a high classification accuracy of 95.6% with only 1292 feature vector sizes for holdout validation. In the fivefold cross-validation, the proposed model slightly increased the classification accuracy, as presented in Figure 6b and Table 4. The model correctly predicted 811 out of 824 pituitary gland tumor class MRI images with a TPR of 98.1%. Another brain MRI dataset comprising 233 patients was used to validate the adaptability and accuracy [63]. A total of 3064 brain MRI scans were obtained at two hospitals in China (Nanfang Hospital and General Hospital), of which 1426 images comprised glioma tumors, 708 comprised meningioma tumors, and 930 comprised pituitary gland tumors [64]. The results of the proposed approach for the new dataset are presented in Figure 7 and Table 5.    The results presented in Figure 7 and Table 5 demonstrate the adaptability and high classification performance of the proposed approach. As presented in Table 6, the results of the proposed WBM-DLNets approach were also compared with those reported in the latest literature.
Recently, the use of machine learning techniques in medical imaging for diagnostic applications has increased. Several researchers have investigated various learning techniques for detecting brain tumors using MRI images [28,29,32,65].

Reference Accuracy (%)
Almalki et al. [18] 95.33 Abiwinanda et al. [27] 84. 19 Irmak [29] 92.66 Kang et al. [32] 93.72 Rehman et al. [65] 95.86 WBM-DLNets (Proposed) 95.7 and 96.7 Deep learning networks have a very high level of accuracy in classifying brain MRI images [28,29]. Irmak [29] proposed a brain tumor detection CNN model that yielded an accuracy of 92.66% for subclassification. Additionally, a pretrained deep learning network has been utilized to detect brain tumors [65]; however, the model training it is too time-consuming. Another study [32] concatenated the deep features of various pretrained models and achieved 93.72% accuracy. The feature vector was excessively large and contained various redundant features. Filter-based feature reduction approaches have also been reported to enhance classification performance [18]. Filtering strategies select features based on their applicability to the dependent variables. However, they do not consider how they affect the model performance. By contrast, wrapper approaches test the effectiveness of a feature subset by training the model with them. Occasionally, a threshold value must be selected to remove unnecessary data in filter-based methods. Wrapper-based strategies have been shown to be more accurate in classifying data. Therefore, in this study, a WBM-DLNet feature optimization approach was proposed to improve the classification performance of brain tumor detection. The WBM-DLNet feature optimization approach and previously published studies are compared in Table 6. The findings revealed that the proposed WBM-DLNet feature optimization technique outperforms competing methods in terms of classification rate. The proposed brain tumor detection approach may help physicians identify tumors quickly and effectively.

Conclusions
In this study, WBM-DLNet feature optimization algorithms were utilized to enhance brain tumor detection classification performance. The deep features of the 16 pretrained deep learning networks were computed. Eight metaheuristic optimization algorithms (MPA, ASOA, HHOA, BOA, WOA, GWOA, BA, and FA) were applied to determine the optimal deep features of all networks using the SVM-based cost function. All metaheuristic optimization algorithms significantly enhanced the classification performance and reduced the feature vector size of each pretrained model. Subsequently, a deep-learning network selection approach was applied to determine the best deep features. The best deep features were concatenated to train the SVM model. The model exhibited the highest classification rate of 95.7% with DenseNet-201-GWOA and EfficientNet-b0-ASOA deep feature-trained SVM models. The model was further validated using a new dataset and exhibited a high classification performance of 96.7%. Therefore, the proposed WBM-DLNet feature optimization algorithm can be considered useful for automatic brain tumor detection.